%I #31 May 15 2022 07:32:15
%S 1,6561,1679616,100000000,2562890625,37822859361,377801998336,
%T 2821109907456,16815125390625,83733937890625,360040606269696,
%U 1370114370683136,4702525276151521,14774554437890625,42998169600000000,117033789351264256,300283484326400961
%N Number of 8-dimensional cage assemblies.
%D Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
%H Clifford A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&format=complete">Zentralblatt review</a>.
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
%F G.f.: -x*(x^14 +6544*x^13 +1568215*x^12 +72338144*x^11 +1086859301*x^10 +6727188848*x^9 +19323413187*x^8 +27306899520*x^7 +19323413187*x^6 +6727188848*x^5 +1086859301*x^4 +72338144*x^3 +1568215*x^2 +6544*x +1)/(x-1)^17. - _Colin Barker_, Jul 09 2012
%F From _Peter Bala_, Jul 02 2019 (Start)
%F a(n) = (n*(n + 1)/2)^8.
%F a(n) = (1/16)*( S(9,n) + 7*S(11,n) + 7*S(13,n) + S(15,n) ), where S(r,n) = Sum_{k = 1..n} k^r. Cf. A059977 and A059978. (End)
%F From _Amiram Eldar_, May 15 2022: (Start)
%F Sum_{n>=1} 1/a(n) = 146432*Pi^2 + 5632*Pi^4/3 + 2048*Pi^6/105 + 256*Pi^8/4725 - 1647360.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1647360 - 1757184*log(2) - 304128*zeta(3) - 57600*zeta(5) - 4032*zeta(7). (End)
%t m = 8; Table[n^m (n + 1)^m/2^m, {n, 1, 18}]
%Y Cf. A059827, A059860, A059977, A059978, A091043.
%K nonn,easy
%O 1,2
%A _Robert G. Wilson v_, Mar 06 2001